Most of these countries were Islamic a long time before 1960 though.
The increase is due to raisingliving standards . There is much less infant mortality, people are living longer, people are eating more, better food, doing less dangerous jobs etc.
150 years ago, Britain was the most powerful and advanced nation on earth, and 75% of the population were living hand to mouth I.e. they only earned enough in a day to feed themselves that day.
These days not even many poor countries would be like that.